Respuesta :
Answer:
(a)Therefore the charge of each particle is [tex]4.56\times 10^{-4} \ C[/tex].
(b)Therefore the mass of particle 2 is 3.25×10⁻⁶ Kg.
Explanation:
Given that, two positive charges particles are equal charge and the distance between them is 2.60×10⁻² m²
The acceleration of the first particle is 4.60×10³ m/s².
The acceleration of the second particle is 8.50×10³ m/s².
The mass of the first particle is 6.00×10⁻⁶kg.
The coulombs Law:
[tex]F=\frac{kq_1q_2}{r^2}[/tex]
F= Force between the charges.
[tex]q_1 \ and \q_2[/tex]= The charges
r= Distance between the changes.
Here [tex]q_1 =q_2=q[/tex] ,r = 2.60×10⁻² m[tex]k=9\times 10^9[/tex] Nm²/C²
Therefore
[tex]F=9\times 10^9.\frac{q^2}{(2.60\times 10^{-2})^2}[/tex]
=1.33×10¹³ ×q² N.
Again we know that,
Force = mass× acceleration
For the first particle m₁=6.00×10⁻⁶kg, a₁= 4.60×10³ m/s² and F =1.33×10¹³ ×q² N
∴1.33×10¹³ ×q² =6.00×10⁻⁶×4.60×10³
[tex]\Rightarrow q^2=\frac{6.00\times 10^{-6}\times 4.60\times 10^3}{1.33\times 10^{13}}[/tex]
[tex]\Rightarrow q^2= 20.75\times 10^{-16}[/tex]
[tex]\Rightarrow q=4.56\times 10^{-4}[/tex] C
Therefore the charge of each particle is [tex]4.56\times 10^{-4} \ C[/tex].
(b)
To find the mass of the second particle we use the following formula,
Force = mass× acceleration
Here F=m₁a₁, mass = m₂, acceleration= a₂=8.50×10³ m/s².
m₁a₁= m₂a₂
⇒(6.00×10⁻⁶)×( 4.60×10³)= m₂×(8.50×10³)
[tex]\Rightarrow m_2=\frac {(6.00\times10^{-6})\times( 4.60\times10^{3})}{(8.50\times10^3)}[/tex]
=3.25×10⁻⁶ Kg.
Therefore the mass of particle 2 is 3.25×10⁻⁶ Kg.
